# How do you use substitution to solve 3x - 2y = 2 and  x = 3y - 11?

Jan 16, 2018

$x = 4$
$y = 5$

#### Explanation:

Substitution is done by choosing what variable has provided the easiest way to do the process. Since, the second equation $x = 3 y - 11$; where value of x is already provided, it's convenient to solve the value of $y$ first; that is,

$3 x - 2 y = 2 \to e q .1$
$x = 3 y - 11 \to e q .2$

$3 x - 2 y = 2$
where $x = 3 y - 11$, Now plug in the value of x

$3 \left(3 y - 11\right) - 2 y = 2$, distribution property

$9 y - 33 - 2 y = 2$, combine like terms

$9 y - 2 y = 2 + 33$, simplify the equation

$7 y = 35$. divide both sides by 7 to isolate the $y$

$\frac{\cancel{7} y}{\cancel{7}} = \frac{\cancel{35} 5}{\cancel{7}}$

$y = 5$

Now, find the value of $x$ using the second equation and plug in the value of $y = 5$:

$x = 3 y - 11$

$x = 3 \left(5\right) - 11$

$x = 15 - 11$

$x = 4$

Checking:

where: $x = 4 \text{and } y = 5$

$E q .1 :$
$3 x - 2 y = 2$
$3 \left(4\right) - 2 \left(5\right) = 2$
$12 - 10 = 2$
$2 = 2$

$E q .2 :$
$x = 3 y - 11$
$4 = 3 \left(5\right) - 11$
$4 = 15 - 11$
$4 = 4$

Jan 16, 2018

$7 y - 33$ is the answer when you substitute $x$ and simplify.

#### Explanation:

You substitute the $x$ with $3 y - 11$ and keep simplifying until you get the answer. Here are the steps:

$3 \left(3 y - 11\right) - 2 y = 2$

(Then you distribute/ multiply 3 by what's inside the parentheses.)

$9 y - 33 - 2 y = 2$

(It may seem like you have your answer, but not yet! Hmm... it seems like there are two "y's", huh?)

$7 y - 33$

(I just did $9 y - 7 y$)

$7 y - 33$ is the answer.

My source is my knowledge.
I hope that helped you!